Problem: Solve for $x$ and $y$ using substitution. ${-5x+2y = -11}$ ${y = -2x-10}$
Explanation: Since $y$ has already been solved for, substitute $-2x-10$ for $y$ in the first equation. ${-5x + 2}{(-2x-10)}{= -11}$ Simplify and solve for $x$ $-5x-4x - 20 = -11$ $-9x-20 = -11$ $-9x-20{+20} = -11{+20}$ $-9x = 9$ $\dfrac{-9x}{{-9}} = \dfrac{9}{{-9}}$ ${x = -1}$ Now that you know ${x = -1}$ , plug it back into $\thinspace {y = -2x-10}\thinspace$ to find $y$ ${y = -2}{(-1)}{ - 10}$ $y = 2 - 10$ $y = -8$ You can also plug ${x = -1}$ into $\thinspace {-5x+2y = -11}\thinspace$ and get the same answer for $y$ : ${-5}{(-1)}{ + 2y = -11}$ ${y = -8}$